Recent years of research have shown that the complex temporal structure of ongoing
oscillations is scale-free and characterized by long-range temporal correlations. Detrended …

This paper introduces coordinate-independent methods for analyzing multiscale dynamical
systems using numerical techniques based on the transfer operator and its adjoint. In …

In this second volume, a general approach is developed to provide approximate
parameterizations of the" small" scales by the" large" ones for a broad class of stochastic …

A framework for the study of surface ocean inertial particle motion is built from the Maxey–
Riley set. A new set is obtained by vertically averaging each term of the original set, adapted …

The intriguing figure from the previous page presents a visualization of the type of manifolds
this monograph is concerned with. First, obtained as a graph over some chosen linearized …

Currently the number of reduction methods used in practice in climate applications is vast
and tends to be difficult to access for researchers searching for an overview of the area. In …

Multi-time-scale stochastic dynamical systems are ubiquitous in science and engineering,
and the reduction of such systems and their models to only their slow components is often …

Abstract Systems composed of large numbers of interacting agents often admit an effective
coarse-grained description in terms of a multidimensional stochastic dynamical system …

Covariance inflation is an ad hoc treatment that is widely used in practical real-time data
assimilation algorithms to mitigate covariance underestimation owing to model errors …

Computational studies often proceed from the premise that cortical dynamics operate in a
linearly stable domain, where fluctuations dissipate quickly and show only short memory …